Final Exam - Triangles and Transformations

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What are the criteria for triangle congruence?

Back

The criteria for triangle congruence are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side).

Front

What is the SSS congruence criterion?

Back

SSS (Side-Side-Side) states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What is the SAS congruence criterion?

Back

SAS (Side-Angle-Side) states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What is the ASA congruence criterion?

Back

ASA (Angle-Side-Angle) states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Front

What is the AAS congruence criterion?

Back

AAS (Angle-Angle-Side) states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the SSA condition in triangles?

Back

SSA (Side-Side-Angle) is not a valid criterion for triangle congruence, as it can lead to ambiguous cases where two different triangles can be formed.

Front

How do you reflect a point over the y-axis?

Back

To reflect a point (x, y) over the y-axis, change the sign of the x-coordinate: the new point is (-x, y).

Front

How do you reflect a point over the x-axis?

Back

To reflect a point (x, y) over the x-axis, change the sign of the y-coordinate: the new point is (x, -y).

Front

Can a triangle have sides of lengths 3, 4, and 9?

Back

No, a triangle cannot have sides of lengths 3, 4, and 9 because the sum of the lengths of any two sides must be greater than the length of the third side.